If you’ve recently withdrawn cash from an ATM on St John Street in London, you might have been interrupted in your everyday routine by noticing a small sign. The cashpoint was invented in 1967, the sign informs you, by John Shepherd-Barron, who came up with the idea after using a chocolate vending machine. And there you were, thinking cashpoints were boring.

Well, they are boring – just like the manhole cover at Clerkenwell Close or the bricks at Bleeding Heart Lane, where you’ll see similar signs – but that doesn’t mean they’re not significant. That’s the point being made by the Museum of the Mundane, or MoMu, a pun on New York’s Museum of Modern Art. MoMu is pitched as MoMa’s opposite, celebrating the urban ordinary.

It’s a simple idea: affix museum-style labels on to mundane city objects (traffic lights, bollards, black cabs) as a way of drawing attention to their hidden importance. MoMu may be a glorified ad for the branding agency that created it, but it nevertheless raises an interesting point: perhaps it’s less the famous towers or historic districts that define a city, but rather the mundane objects encountered at every street corner. Together, boring objects accumulate to form a richer image of the city than the one you see in tourist brochures. They’re the special Lego blocks you only get with the big set called London or Rio or Manila.

What’s more, mundane city objects also offer a glimpse into the operational logic of a city. Pedestrian buttons, building materials or the Johnston typeface are the visible moments when vast urban systems reveal themselves. They are the hooks that invite our participation in the system. Despite or because of their mundanity, they are the city – as close as we can get to this big machine we inhabit.

The idea that the whole city is a museum if only you know how to look is not necessarily a new one. In 1966 architect Robert Venturi argued there’s as much to learn from the commercial architecture of the Las Vegas strip as there is from the great buildings of Venice or Rome. It’s a call to suspend aesthetic judgments of class and taste, and to recognise significance within the apparently insignificant. A similar project in New York called Mmuseumm also seeks to elevate mundane objects. A tiny gallery, merely 2 x 2 metres square, it occupies a disused lift shaft in a dingy back lane of Manhattan’s Tribeca. Objects range from the truly banal (“toothpaste tubes from around the world”, “mosquitos killed mid-bite”) to the politically significant, but no less banal (“pool toy packaging subjected to Saudi censorship”, “shoe thrown at George Bush by an Iraqi journalist in 2008”). Creator Alex Kalman describes his project as “contemporary archaeology”.

Whatever you think of these projects (does it matter that the traffic light MoMu celebrates was actually designed in 1965, not 1868 as the label claims? Kind of, yes), noticing city objects “in the wild” can jolt you out of the moment to reflect on the millions of design decisions that bring the city into being. Boring objects can teach us that the city is an intentionally constructed project – and therefore a project that can be changed for the better.

Rory Hyde is the curator of contemporary architecture and urbanism at the Victoria and Albert Museum, London.